Solutions for quasilinear Schrödinger systems with critical exponents

Abstract

This paper deals with a class of quasilinear Schrödinger system with critical exponents and bounded potentials inwhereis the coupling term with critical growth, and a(x), b(x) are potential functions. This kind of equations include the so-called Modified Nonlinear Schrödinger Systems. By using a perturbation method, we prove the existence of a ground state positive solution for (P ).Mathematics Subject Classification. 35B05 · 35B45.

Concentration of ground state solutions for quasilinear Schrödinger systems with critical exponents

“…Thus, from the view point of mathematics, we are lead to consider the quasilinear systems. For example, Guo and Li [9] proved the existence of a ground state positive solution for a class of quasilinear Schrodinger system with critical exponents by perturbation method. We also refer to [11,10] and references therein for more related results on the quasilinear systems.…”